Rinse, pat dry and lightly brush chicken breasts with oil. Season with salt and pepper. Slice onion into 1/4-inch thick rings, but do not separate rings. Rinse poblano and pat dry. Place onion, pepper and chicken over medium coals or grill over medium heat 10 to 15 minutes or until vegetables are soft and chicken is done (the juices should run clear). Place pepper in a small paper sack while still hot from the fire and let it cool for 20 minutes. After cooling, peel away skin and scrape out seeds. Chop onion, pepper and chicken into bite-size pieces. Place butter in a large heavy pot over low heat. Add garlic and mushrooms and cook 5 minutes or until softened. Add chopped chicken, onions, poblano pepper, corn and 2 cups water. Mix and simmer for 5 minutes or until softened. Add cubed cheese and simmer until melted. Do not allow to boil. In a separate bowl, dissolve cornstarch with 1/2 cup water. Stir dissolved cornstarch into remaining 1 1/2 cups of water. Add to soup, stirring constantly, and cook over low heat until thickened. Makes 8 servings.